Related papers: Quantum Volunteer's Dilemma
In an inverse game problem, one needs to infer the cost function of the players in a game such that a desired joint strategy is a Nash equilibrium. We study the inverse game problem for a class of multiplayer matrix games, where the cost…
Game theory is a well established branch of mathematics whose formalism has a vast range of applications from the social sciences, biology, to economics. Motivated by quantum information science, there has been a leap in the formulation of…
We study how strategic interaction can arise from controlled quantum dynamics rather than being imposed as an external mathematical structure. We introduce a class of interaction-defined quantum games in which players are represented by…
This paper explores the Nash equilibria of a variant of the Colonel Blotto game, which we call the Asymmetric Colonel Blotto game. In the Colonel Blotto game, two players simultaneously distribute forces across $n$ battlefields. Within each…
Several quantum versions of the battle of the sexes game are analyzed. Some of them are shown to reproduce the classical game. In some, there are no Nash quantum pure equilibria. In some others, the payoffs are always equal to each other.…
We consider shared workspace scenarios with humans and robots acting to achieve independent goals, termed as parallel play. We model these as general-sum games and construct a framework that utilizes the Nash equilibrium solution concept to…
The interaction of competing agents is described by classical game theory. It is now well known that this can be extended to the quantum domain, where agents obey the rules of quantum mechanics. This is of emerging interest for exploring…
In strategic games such as the prisoner's dilemma, allowing players to make binding offers of utility transfers before play has been shown to alter incentives and potentially support cooperative outcomes. These preplay exchange mechanisms…
An example of the macroscopic game of two partners consisting of two classical games played simultaneously with special dependence of strategies is considered. The average profit of each partner is equal to the average profit obtained in…
We consider multi-agent decision making, where each agent optimizes its cost function subject to constraints. Agents' actions belong to a compact convex Euclidean space and the agents' cost functions are coupled. We propose a distributed…
Cooperative dynamics are central to our understanding of many phenomena in living and complex systems. However, we lack a universal mechanism to explain the emergence of cooperation. We present a novel framework for modelling social dilemma…
We consider a tournament among four equally strong semifinalists. The players have to decide how much stamina to use in the semifinals, provided that the rest is available in the final and the third-place playoff. We investigate optimal…
This paper considers a two-player game where each player chooses a resource from a finite collection of options. Each resource brings a random reward. Both players have statistical information regarding the rewards of each resource.…
In recent years methods have been proposed to extend classical game theory into the quantum domain. This paper explores further extensions of these ideas that may have a substantial potential for further research. Upon reformulating quantum…
The concept of forming harmonious coalitions is introduced to both classical and quantum symmetric cooperative game. In both cases, players are motivated to form coalitions. Also, the main feature of the cooperative game is conserved.
We quantize prisoner dilemma in presence of collective dephasing with dephasing rate $\gamma $. It is shown that for two parameters set of strategies $Q\otimes Q$ is Nash equilibrium below a cut-off value of time. Beyond this cut-off it…
In general, Nash equilibria in normal-form games may require players to play (probabilistically) mixed strategies. We define a measure of the complexity of finite probability distributions and study the complexity required to play Nash…
We give a strict mathematical description for a refinement of the Marinatto-Weber quantum game scheme. The model allows the players to choose projector operators that determine the state on which they perform their local operators. The game…
Is there an algorithm that takes a game in normal form as input, and outputs a Nash equilibrium? If the payoffs are integers, the answer is yes, and lot of work has been done in its computational complexity. If the payoffs are permitted to…
We introduce a novel class of Nash equilibrium seeking dynamics for non-cooperative games with a finite number of players, where the convergence to the Nash equilibrium is bounded by a KL function with a settling time that can be upper…